Abstract

In 1971, Golinskii and Ibragimov proved that if the Verblunsky coefficients, {α_n}_n^∞ = 0, of a measure dμ on ∂D obey ∑_(n=0)^∞^n│α_n│^2 < ∞, then the singular part, dμs, of dμ vanishes. We show how to use extensions of their ideas to discuss various cases where ∑_(n=0)^N^n│α_n│^2 diverges logarithmically. As an application, we provide an alternative to a part of the proof of a recent theorem of Damanik and Killip.